AP EAMCET · Maths · Hyperbola
If a circle of radius 4 cm passes through the foci of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{4}=1\) and concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is
- A \(2\)
- B \(2 \sqrt{3}\)
- C \(\frac{2}{\sqrt{3}}\)
- D \(\sqrt{3}\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
Given that circle passes through foci of given hyperbola and have radius 4 . \(\therefore \quad c=4\) and \(b=2\) [ from equation of hyperbola] \(\because \quad a^2+b^2=c^2 \Rightarrow a^2+4=16 \Rightarrow a=2 \sqrt{3}\) For congugate hyperbola \(a=2\) and \(c=4\)…
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